E2 VoC Analyses Part 3: RL Analyses

AIC average by age group

Examine age-related change in parameter estimates from models

Run regressions between model parameters and age

## 
## Call:
## lm(formula = LL ~ age, data = model_params)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -157.706  -55.851    8.701   52.092  131.154 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -243.141     19.401 -12.532   <2e-16 ***
## age            2.813      1.149   2.448   0.0157 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 67.27 on 133 degrees of freedom
## Multiple R-squared:  0.04313,    Adjusted R-squared:  0.03593 
## F-statistic: 5.994 on 1 and 133 DF,  p-value: 0.01565

## 
## Call:
## lm(formula = alphaPosChoice ~ age, data = model_params)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.28765 -0.19218 -0.08989  0.12089  0.68734 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.863e-01  7.683e-02   3.727 0.000286 ***
## age         8.182e-05  4.551e-03   0.018 0.985681    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2664 on 133 degrees of freedom
## Multiple R-squared:  2.431e-06,  Adjusted R-squared:  -0.007516 
## F-statistic: 0.0003233 on 1 and 133 DF,  p-value: 0.9857

## 
## Call:
## lm(formula = alphaNegChoice ~ age, data = model_params)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.19615 -0.12346 -0.06146  0.00172  0.82184 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.29767    0.06518   4.567 1.12e-05 ***
## age         -0.01183    0.00386  -3.064  0.00264 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.226 on 133 degrees of freedom
## Multiple R-squared:  0.06595,    Adjusted R-squared:  0.05892 
## F-statistic:  9.39 on 1 and 133 DF,  p-value: 0.002642

## 
## Call:
## lm(formula = alphaPosComp ~ age, data = model_params)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20486 -0.16290 -0.11220  0.01203  0.87932 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.261130   0.077306   3.378 0.000959 ***
## age         -0.006186   0.004579  -1.351 0.178941    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.268 on 133 degrees of freedom
## Multiple R-squared:  0.01354,    Adjusted R-squared:  0.006124 
## F-statistic: 1.826 on 1 and 133 DF,  p-value: 0.1789

## 
## Call:
## lm(formula = alphaNegComp ~ age, data = model_params)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.2291 -0.2075 -0.1851  0.1059  0.7982 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.253218   0.095197   2.660  0.00878 **
## age         -0.002721   0.005638  -0.483  0.63020   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3301 on 133 degrees of freedom
## Multiple R-squared:  0.001748,   Adjusted R-squared:  -0.005758 
## F-statistic: 0.2329 on 1 and 133 DF,  p-value: 0.6302

## 
## Call:
## lm(formula = betaAgency ~ age, data = model_params)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -9.553 -4.101 -1.937  3.475 19.945 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  3.91959    1.65918   2.362   0.0196 *
## age          0.24602    0.09827   2.504   0.0135 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.753 on 133 degrees of freedom
## Multiple R-squared:  0.04501,    Adjusted R-squared:  0.03783 
## F-statistic: 6.268 on 1 and 133 DF,  p-value: 0.0135

## 
## Call:
## lm(formula = betaMachine ~ age, data = model_params)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.060 -3.211 -1.095  1.786 22.739 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  4.89653    1.45762   3.359  0.00102 **
## age          0.15066    0.08633   1.745  0.08327 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.054 on 133 degrees of freedom
## Multiple R-squared:  0.02239,    Adjusted R-squared:  0.01504 
## F-statistic: 3.046 on 1 and 133 DF,  p-value: 0.08327

## 
## Call:
## lm(formula = agencyBonus ~ age, data = model_params)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.78412 -0.22038 -0.11946  0.06671  2.45157 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.663550   0.150879   4.398 2.22e-05 ***
## age         -0.014854   0.008936  -1.662   0.0988 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5231 on 133 degrees of freedom
## Multiple R-squared:  0.02035,    Adjusted R-squared:  0.01299 
## F-statistic: 2.763 on 1 and 133 DF,  p-value: 0.09882

Learning rate model

## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: estimate ~ age_z * valence * agency + (1 | subject_id)
## Data: learning_rates
##                 Effect        df         F p.value
## 1                age_z 1, 133.00    3.75 +    .055
## 2              valence 1, 399.00   8.68 **    .003
## 3               agency 1, 399.00      0.28    .596
## 4        age_z:valence 1, 399.00      0.89    .345
## 5         age_z:agency 1, 399.00      0.10    .751
## 6       valence:agency 1, 399.00 25.75 ***   <.001
## 7 age_z:valence:agency 1, 399.00    2.96 +    .086
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: estimate ~ age_z * valence * agency + (1 | subject_id)
##    Data: data
## 
## REML criterion at convergence: 180.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.4215 -0.6024 -0.3468  0.1215  3.2414 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept) 0.007237 0.08507 
##  Residual               0.068473 0.26167 
## Number of obs: 540, groups:  subject_id, 135
## 
## Fixed effects:
##                          Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)              0.191380   0.013432 133.000000  14.248  < 2e-16 ***
## age_z                   -0.026041   0.013444 133.000000  -1.937  0.05486 .  
## valence1                -0.033171   0.011261 399.000000  -2.946  0.00341 ** 
## agency1                  0.005975   0.011261 399.000000   0.531  0.59600    
## age_z:valence1          -0.010648   0.011271 399.000000  -0.945  0.34537    
## age_z:agency1           -0.003581   0.011271 399.000000  -0.318  0.75086    
## valence1:agency1        -0.057139   0.011261 399.000000  -5.074 5.97e-07 ***
## age_z:valence1:agency1  -0.019387   0.011271 399.000000  -1.720  0.08619 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age_z valnc1 agncy1 ag_z:v1 ag_z:g1 vln1:1
## age_z       0.000                                            
## valence1    0.000  0.000                                     
## agency1     0.000  0.000 0.000                               
## age_z:vlnc1 0.000  0.000 0.000  0.000                        
## age_z:gncy1 0.000  0.000 0.000  0.000  0.000                 
## vlnc1:gncy1 0.000  0.000 0.000  0.000  0.000   0.000         
## ag_z:vln1:1 0.000  0.000 0.000  0.000  0.000   0.000   0.000

## 
##  Paired t-test
## 
## data:  model_params$alphaPosChoice and model_params$alphaNegChoice
## t = 6.4697, df = 134, p-value = 1.698e-09
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  0.1254031 0.2358366
## sample estimates:
## mean difference 
##       0.1806199

## 
##  Paired t-test
## 
## data:  model_params$alphaPosComp and model_params$alphaNegComp
## t = -1.1817, df = 134, p-value = 0.2394
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.12816925  0.03229399
## sample estimates:
## mean difference 
##     -0.04793763

Plot relations between model parameters and age